$\int z^7\,dz=$ $+C$
Answer: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int z^{{7}}\,dz&=\dfrac{z^{{7}+1}}{{7}+1}+C \\\\ &=\dfrac18 z^8+C \end{aligned}$ In conclusion, $\int z^7\,dz=\dfrac18 z^8+C$